21 research outputs found
Truncated post-Newtonian neutron star model
As a preliminary step towards simulating binary neutron star coalescing
problem, we test a post-Newtonian approach by constructing a single neutron
star model. We expand the Tolman-Oppenheimer-Volkov equation of hydrostatic
equilibrium by the power of , where is the speed of light, and
truncate at the various order. We solve the system using the polytropic
equation of state with index and 3, and show how this
approximation converges together with mass-radius relations. Next, we solve the
Hamiltonian constraint equation with these density profiles as trial functions,
and examine the differences in the final metric. We conclude the second
`post-Newtonian' approximation is close enough to describe general relativistic
single star. The result of this report will be useful for further binary
studies.
(Note to readers) This paper was accepted for publication in Physical Review
D. [access code dsj637]. However, since I was strongly suggested that the
contents of this paper should be included as a section in our group's future
paper, I gave up the publication.Comment: 5 pages, RevTeX, 3 eps figs, epsf.sty, accepted for publication in
PRD (Brief Report), but will not appea
Post-Newtonian Models of Binary Neutron Stars
Using an energy variational method, we calculate quasi-equilibrium
configurations of binary neutron stars modeled as compressible triaxial
ellipsoids obeying a polytropic equation of state. Our energy functional
includes terms both for the internal hydrodynamics of the stars and for the
external orbital motion. We add the leading post-Newtonian (PN) corrections to
the internal and gravitational energies of the stars, and adopt hybrid orbital
terms which are fully relativistic in the test-mass limit and always accurate
to PN order. The total energy functional is varied to find quasi-equilibrium
sequences for both corotating and irrotational binaries in circular orbits. We
examine how the orbital frequency at the innermost stable circular orbit
depends on the polytropic index n and the compactness parameter GM/Rc^2. We
find that, for a given GM/Rc^2, the innermost stable circular orbit along an
irrotational sequence is about 17% larger than the innermost secularly stable
circular orbit along the corotating sequence when n=0.5, and 20% larger when
n=1. We also examine the dependence of the maximum neutron star mass on the
orbital frequency and find that, if PN tidal effects can be neglected, the
maximum equilibrium mass increases as the orbital separation decreases.Comment: 53 pages, LaTex, 9 figures as 10 postscript files, accepted by Phys.
Rev. D, replaced version contains updated reference
Dynamics of a thin shell in the Reissner-Nordstrom metric
We describe the dynamics of a thin spherically symmetric gravitating shell in
the Reissner-Nordstrom metric of the electrically charged black hole. The
energy-momentum tensor of electrically neutral shell is modelled by the perfect
fluid with a polytropic equation of state. The motion of a shell is described
fully analytically in the particular case of the dust equation of state. We
construct the Carter-Penrose diagrams for the global geometry of the eternal
black hole, which illustrate all possible types of solutions for moving shell.
It is shown that for some specific range of initial parameters there are
possible the stable oscillating motion of the shell transferring it
consecutively in infinite series of internal universes. We demonstrate also
that this oscillating type of motion is possible for an arbitrary polytropic
equation of state on the shell.Comment: 17 pages, 7 figure
Rotating Stars in Relativity
Rotating relativistic stars have been studied extensively in recent years,
both theoretically and observationally, because of the information one could
obtain about the equation of state of matter at extremely high densities and
because they are considered to be promising sources of gravitational waves. The
latest theoretical understanding of rotating stars in relativity is reviewed in
this updated article. The sections on the equilibrium properties and on the
nonaxisymmetric instabilities in f-modes and r-modes have been updated and
several new sections have been added on analytic solutions for the exterior
spacetime, rotating stars in LMXBs, rotating strange stars, and on rotating
stars in numerical relativity.Comment: 101 pages, 18 figures. The full online-readable version of this
article, including several animations, will be published in Living Reviews in
Relativity at http://www.livingreviews.org